In order to increase the amount of exercise in her daily routine, Tara decides to walk up the seven flights of stairs to her car instead of taking the elevator. Each of the steps she takes are 18.0 cm high, and there are 12 steps per flight. (a)
If Tara has a mass of 61.5 kg, what is the change in the gravitational potential energy of the Tara-Earth system (in J) when she reaches her car?

(b)
If the human body burns 1.5 Calories (6.28 ✕ 103 J) for each ten steps climbed, how much energy (in J) has Tara burned during her climb?

(c)
How does the energy she burned compare to the change in the gravitational potential energy of the system?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit